Well since Minecraft doesn't require a lot of resources a kit like this which contains all the parts you need AMD A8-6600K 3.9GHz Quad-Core APU/MSI A58M-E33 mATX MB/4GB DDR3 1600 ADATA XPG V1 Memory/1TB WD Blue 7200rpm SATA HDD/2X LED Case Fan/Ultra XBlaster V2 Case w/450W PSU Barebones at TigerDirect.com and a graphics card MSI R7 240 2GD3 LP Radeon R7 240 Graphic Card - 730 MHz Core - 2 GB DDR3 SDRAM - PCI Express 3.0 x16 - Low-profile (Refurbished) at TigerDirect.com..
Much better spec package than the one I mentioned, the only downside being it doesn't come with Windows... goes to show how much money we have to waste on the OS!